Kitaev honeycomb antiferromagnet in a field: quantum phase diagram for general spin

We combine tensor-network approaches and high-order linked-cluster expansions to investigate the quantum phase diagram of the antiferromagnetic Kitaev's honeycomb model in a magnetic field for general spin values. For the pure Kitaev model, tensor network calculations confirm the absence of fluxes and spin-spin correlations beyond nearest neighbor in the ground state, but signal a breaking of the discrete orientational symmetry for $S\in\{1,3/2,2\}$ inline with the semiclassical limit. An intermediate region between Kitaev phases and the high-field polarized phase is demonstrated for all considered spin values. In this intermediate region the tensor network results display a sequence of potential phases whose number increases with the spin value. Each of these can be characterized by distinct local magnetization patterns while the total magnetization increases smoothly as a function of the field. The analysis of the high-field zero-momentum gap and the associated spectral weight of the polarized phase for general spin $S$ obtained by linked-cluster expansions is consistent with an unconventional quantum critical breakdown of the high-field polarized phase in accordance with the presence of exotic physics at intermediate Kitaev couplings.